Rhinos skipper Sinfield did go over soon after, following up his own up-and-under to score.
Sinfield then added two further points after Warrington conceded a penalty before the hosts found another try, this time Ben Jones-Bishop holding off a couple of challenges on the right wing to score.
Warrington managed to level up the scores just before the break when Joel Monaghan squeezed over in the 37th minute.
Ryan Atkins then put the Wolves ahead but Hodgson couldn't add the extras.
Carl Ablett brought the scores level and Sinfield was able to kick the extra two points as Leeds edged ahead 18-20.
Ablett went from scorer to provider in the 71st minute, finding Ryan Hall on the left to go over and once again Sinfield's right boot found the middle of the posts.
The Rhinos finished just fifth in the Super League but repeated last year's heroics by winning eight on the bounce in the playoffs to reach the final.